At one time I had a "gorilla" monopod shooting stick I was going to try out as a walking stick. It broke first time out. Moved to trekking poles after that...anyhow.... I took the top section of that and use it on my knee/thigh/waist/tree/etc. It's only a few oz's and provides a point of contact to steady. It's helped me thread bullets through some small windows in cover.
Wouldn't help you with your back to the tree, but I killed two does this past weekend at 140 and 120 yards respectively using the Tethrd HYS Strap and two of the new Fold n Go hangers. Worked great as a rifle rest and both does bang flopped. Most of my saddle rifle shots have been within 75 yards and generally free hand, so I was thrilled with how good of a rest I was able to get with this set up leaning into the tree in a sitting position.
I think going with the rope set up as mentioned above would work well for a traditional hang on, or going with a monopod/tripod like the Primos trigger stick. Practicing free hand shots would be beneficial as well.
Killed a lot of deer with my left elbow propped on my left knee too.
I bought the bow hanger from genesis 3D printing. Drilled out the top hole and put it in I think 5/16 amsteel. I can slip it around the tree as I need on back of tee shots. I can also kneel in my hang on and use the seat. Lastly I use as I can knees and legs but my kid shoots competition rifle and he has a trick of if standing to kick it out of gear and wedge the bicep to the side above the hip bone. Like a built in tripod. I also agree with free hand practice.
Primos monopod with tree stand attachment base. If you have a front rail, lean your monopod forward until you rest it in the rail. If an open stand, use the leg strap that comes with it.